The present invention relates to spectral estimation of non-deterministic signals and, more particularly, to a more robust method for estimating spectral components of incomplete and/or noisy input signal records.
It is known to utilize a maximum entropy method for estimation of spectral components of a signal, as originally discussed by J. P. Burg in "Maximum Entropy Spectral Analysis", Proc. 37th Meeting Society Exploration Geophysicist (1967), but such spectral estimators exhibit severe degradation from either noisy or short input data records if autoregressive (AR) or autoregressive-moving-average (ARMA) estimation models are utilized. Because spectral estimation methods are useful in a variety of technical applications, including voice recognition, voice and image compression Doppler velocimetry, moving target indication and/or target-bearing estimation (in radar and sonar systems) high resolution spectroscopy for qualitative and quantitative chemical analysis, and the like, it is highly desirable to have a robust spectrum estimation method which can operate even when the incoming sample signaled data records fluctuate due to incompleteness and/or noise. The use of a constrained maximum entropy approach, where a Lagrange multiplier in the constrained extremal value problem can be interpreted as an effective temperature parameter, is known from the work of S. J. Wernecke and L. R. D'Addario, "Maximum Entropy Image Reconstruction", IEEE Trans. Comput., vol C-26, pp 351- 364 (1977); S. F. Gull and G. J. Daniell, "Image Reconstruction From Incomplete and Noisy Data," Nature vol. 272, pp. 686- 690 (1978); and T. J. Cornwell, "A Method of Stabilizing The CLEAN Algorithm, " Astron. Astrophys., vol. 121, pp. 281-285, (1983) wherein two-dimensional spatial-spectral super-resolution radio-astronomy imagery was considered using data generated from large aperture synthesis techniques. In these works, the solution to the state variables were generated either by Newton-Raphson iterative solutions, or by the deployment of a non-linear deconvolution algorithm (with the acronym "CLEAN" as originally introduced by J. Hogbom, in "Aperture Synthesis With a Non-Regular Distribution of Interferometer Baselines," Astrophys. J. Suppl., vol. 15, pp. 417-426, 1974. However, it is desirable to provide a method having not only greater accuracy, but shorter implementation time than either the Newton-Raphson or CLEAN algorithmic solution methods utilized in this prior art.